Topics: The notion of Categorical Abstract Machine (CAM). Evaluation in a Cartesian closed category (c.c.c.). Evaluating map. Environment. Examples of expression evaluation. Collision of variables. Eliminating the collision. De Bruijn's encoding. De Bruijn's numerals. Evaluation in a c.c.c. using De Bruijn's encoding. Combinatory glue. The properties of the theories of computation. Topics: lambda-calculus, combinatory logic, expression evaluation, theory of computation
Book by V.E. Wolfengagen "Applicative computing. Its quarks, atoms and molecules". Edited by Dr. L.Yu. Ismailova. Moscow: “Center JurInfoR”, 2010. -- 62 p. This work covers the advanced topics in main ideas of computing in general. This material is approved in practice of NRNU MEPhI, MIPT and several other educational centers of the Russian Federation. Its 1st part represents an outlook of computations, which is achieved by adoption of the atomic doctrine for specified reference... ( 2 reviews ) Topics: computing, applicative system, combinatory logic, applicative programming, theory of objects
Book by V.E. Wolfengagen "Combinatory Logic in Programming. Computations with Objects Through Examples and Exercises". 2-nd ed. -- Moscow, Center JurInfoR, 2003. X+336 p. The book is intended for computer science students, programmers and professionals who have already got acquainted with the basic courses and background on discrete mathematics. It may be used as a textbook for graduate course on theoretical computer science. The book introduces a reader to the conceptual framework... Topics: Applicative computations, combinatory logic, lambda-calculus, programming, categorical abstract...
Topics: A notion of developing the abstract machine. Functioning of abstract machine. States. Working cycle of the abstract machine. Examples of evaluation. Compiling and executing the code. Topics: lambda-calculus, combinatory logic, expression evaluation, theory of computation
Topics: The ways of evaluation. Running the compiled programming code. Assembling the code. Comparison of the evaluations. Topics: lambda-calculus, combinatory logic, expression evaluation, theory of computation
Topics: Expression evaluation and the ways of evaluating. The representation of the environment of expression evaluation. De Bruijn's theory of computation of expression evaluation. Syntactical theory of computation. The kinds of the expression evaluation theories. Topics: lambda-calculus, combinatory logic, expression evaluation, theory of computation